Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1996-06-30
A Note on the Bonnet-Myers TheoremV. Boju and Louis Funar (1) Universitatea din Craiova, Romania
(2) Université Grenoble I, Saint-Martin-d'Hères, France
The aim of this note is to derive a compactness result for complete manifolds whose Ricci curvature is bounded from below. The classical result, usually stated as Bonnet-Myers theorem, provides an estimation of the diameter of a manifold whose Ricci curvature is greater than a strictly positive constant. Weaker assumptions that the Ricci curvature function tends slowly to zero (when the distance from a fixed point goes to infinity) were already considered in [2, 3]. We shall improve here their results.
Keywords: Ricci curvature, Jacobi equation
Boju V., Funar Louis: A Note on the Bonnet-Myers Theorem. Z. Anal. Anwend. 15 (1996), 275-278. doi: 10.4171/ZAA/698